Finite Group Databasebeta

← Group #309003

Character table — Group #309003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882222444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-11111-1-11-1
χ911111111111111111-1-1-1-111111-1-1111111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-11-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11-111-1-111-1-1-11
χ172222222222-2-2-2-222-22222-20000-2-2000000000022-2-200000000200-200000000
χ182222222222-2-2-2-222-22222-20000-2-20000000000-2-22200000000-200200000000
χ192222222222-2-2-2-222-2-2-2-2-2-2000022000000000022-2-200000000-200200000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000220000000000-2-22200000000200-200000000
χ2122222222-2-22222-2-2-20000-22222002222-2-200000000000000000-2-2000000000
χ2222222222-2-22222-2-2-20000-2222200-2-2-2-2-2-20000000000000000022000000000
χ2322222222-2-22222-2-2-20000-2-2-2-2-20022-2-22200000000000000000-22000000000
χ2422222222-2-22222-2-2-20000-2-2-2-2-200-2-22222000000000000000002-2000000000
χ252222-2-2-2-22222-2-2-2-220000-222-2-20000002-20000000000002-22-2000000000000
χ262222-2-2-2-22222-2-2-2-220000-222-2-20000002-2000000000000-22-22000000000000
χ272222-2-2-2-22222-2-2-2-220000-2-2-222000000-220000000000002-2-22000000000000
χ282222-2-2-2-22222-2-2-2-220000-2-2-222000000-22000000000000-222-2000000000000
χ292222-2-2-2-2-2-222-2-222-22i2i−2i−2i222-2-22i−2i0000-222i2i−2i−2i000000000000000000000000
χ302222-2-2-2-2-2-222-2-222-22i2i−2i−2i2-2-2222i−2i00002-2−2i−2i2i2i000000000000000000000000
χ312222-2-2-2-2-2-222-2-222-2−2i−2i2i2i222-2-2−2i2i0000-22−2i−2i2i2i000000000000000000000000
χ322222-2-2-2-2-2-222-2-222-2−2i−2i2i2i2-2-222−2i2i00002-22i2i−2i−2i000000000000000000000000
χ332222-2-2-2-2-2-2-2-2222222i2i−2i−2i-20000−2i2i000000000000002i2i−2i−2i000000002-2000000
χ342222-2-2-2-2-2-2-2-2222222i2i−2i−2i-20000−2i2i00000000000000−2i−2i2i2i00000000-22000000
χ352222-2-2-2-2-2-2-2-222222−2i−2i2i2i-200002i−2i000000000000002i2i−2i−2i00000000-22000000
χ362222-2-2-2-2-2-2-2-222222−2i−2i2i2i-200002i−2i00000000000000−2i−2i2i2i000000002-2000000
χ3722-2-222-2-2002-22-2000000002-22-2002-22-2000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i200
χ3822-2-222-2-2002-22-2000000002-22-2002-22-2000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i200
χ3922-2-222-2-2002-22-2000000002-22-200-22-22000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i200
χ4022-2-222-2-2002-22-2000000002-22-200-22-22000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i200
χ4122-2-222-2-2002-22-200000000-22-22002-2-22000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i200
χ4222-2-222-2-2002-22-200000000-22-22002-2-22000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i200
χ4322-2-222-2-2002-22-200000000-22-2200-222-2000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i200
χ4422-2-222-2-2002-22-200000000-22-2200-222-2000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ464444-4-4-4-444-4-444-4-4-4000040000000000000000000000000000000000000000
χ4744-4-444-4-400-44-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ4844-4-444-4-400-44-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ4944-4-4-4-444004-4-44000000004-4-44000000000000000000000000000000000000
χ5044-4-4-4-444004-4-4400000000-444-4000000000000000000000000000000000000
χ5144-4-4-4-44400-444-4000000000000000000000000000022−22−22220000000000000000
χ5244-4-4-4-44400-444-40000000000000000000000000000−222222−220000000000000000
χ534-44-44-44-44-400004-40000000000000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-44-44-44-400004-4000000000000000000−2i22i2−2i22i2000000000000000000000000
χ554-44-44-44-4-440000-4404i−4i4i−4i00000000000000000000000000000000000000000
χ564-44-44-44-4-440000-440−4i4i−4i4i00000000000000000000000000000000000000000
χ574-44-4-44-444-40000-4404-4-4400000000000000000000000000000000000000000
χ584-44-4-44-444-40000-440-444-400000000000000000000000000000000000000000
χ594-44-4-44-44-4400004-400000000000000000022−22−2222000000000000000000000000
χ604-44-4-44-44-4400004-4000000000000000000−222222−22000000000000000000000000
χ618-8-888-8-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).